Welcome to the Wefugees Community and thank you for sharing your situation!
As far as I know, marrying in Germany is not dependent on a certain type of resident status. If you hold a residence permit in Italy, you should be allowed to travel (probably up to 90 days) within the EU. This would allow you to travel to Germany for the marriage. However, please note, that I am not familiar with the Italian system. In Germany, for example, you can not be absent for such a long time, if you receive social money.
Your partner should consult the local registry office (Standesamt) for details and to make an appointment for the marriage itself, as soon as you clarified everything.
Please have also a look at our blog, which gives more information on the marriage procedure in Germany and required documents.
I hope this helps and all the best,